Problem: The sum of two angles is $80^\circ$. Angle 2 is $100^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 80}$ ${y = 3x-100}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-100}$ for $y$ in the first equation. ${x + }{(3x-100)}{= 80}$ Simplify and solve for $x$ $ x+3x - 100 = 80 $ $ 4x-100 = 80 $ $ 4x = 180 $ $ x = \dfrac{180}{4} $ ${x = 45}$ Now that you know ${x = 45}$ , plug it back into $ {y = 3x-100}$ to find $y$ ${y = 3}{(45)}{ - 100}$ $y = 135 - 100$ ${y = 35}$ You can also plug ${x = 45}$ into $ {x+y = 80}$ and get the same answer for $y$ ${(45)}{ + y = 80}$ ${y = 35}$ The measure of angle 1 is $45^\circ$ and the measure of angle 2 is $35^\circ$.